In the modern world, separation of powers was first put into practice when the Constitution of the United States was written and ratified. This was the first time that there was a government with a clear separation between its legislative, judicial, and executive branches.
The idea of separation of powers did not come directly from the minds of those writing the Constitution. It had existed to some extent in Ancient Greece and in the Roman Republic. After that, it had been promoted by some of the most important political philosophers of the Enlightenment era. The man who is most clearly connected to this idea was Montesquieu.
You could say, then, that separation of powers in the modern world started with these philosophers and was put into practice by the United States.
John Adams, in a letter to Dr. Benjamin Rush, stated: "I call you to witness that I was the first member of Congress who ventured to come out in public, as I did in January 1776, in my 'Thoughts on Government,' ...in favor of a government with three branches, and an independent judiciary..."